Hasan Hüseyin Uğurlu

A new classification method by using Lorentzian distance metric

In this study, we propose a new algorithm which works in Lorentzian space with a similar sense in the k-NN method. We exploit the distance metric of Lorentzian space in classification problem. It is a special metric which may give a zero distance for far points. To take best benefit from structural and other properties of the Lorentzian space, a special projection over the data sets is applied. By this projection, basic geometrical operations are used; namely translation (shifting), compression and rotation. Our new algorithm does classification according to the nearest neighbor in Lorentzian space. The usability and validity of the proposed classification method is tested by some public data sets such as WHOLE, VERTEBRAL, RELAX, ECOLI. The results are compared with results of well-known classical classification methods such as kNN, LDA, SVM and Bayes. As a result, our proposed algorithm produces more successful results.

Dimensionality reduction based on Lorentzian Manifold for face recognition

Lorentzian geometry is a subject of mathematics and has famous applications in physics, especially in relativity theory. This geometry has interesting features, e.g. one axis has a negative sign in metric definition (time axis). In this study, we try to apply Lorentzian geometry for feature extraction and dimensionality reduction. We use a Lorentzian Manifold (LM) for face recognition and reduce the dimensionality in this new feature space. We compare results with different feature extraction methods; Principal Component Analysis (PCA), Linear Discriminant Analysis (LDA) and Locality Preserving Projection (LPP). Our experiments show that the best feature extraction method is LM and it produces the best face recognition rates. It is also powerful in dimensionality reduction.

Classification with SVM in Lorentzian space

Classification is one of the most researched issues in Machine Learning. In this study, the Lorentzian Support Vector Machine (LSVM) method is proposed that performs classification in Lorentzian space. This proposed new classifier forms a hyperplane separating the classes based on the Lorentzian metric and maximize margins between nearest points to the hyperplane according to the Lorentzian distance. Thus, samples from different classes are classified in Lorentzian space. Also, for the purpose of increasing the classification accuracy, a pre-preprocessing is applied. Experimental results taken from LSVT, SONAR, TELESCOPE and WISCONSIN data sets validate the proposed LSVM method.